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NASA NTRS1983

Shape from Shading: An Assessment

Previous efforts to recover surface shape from image irradiance are reviewed in order to assess what can and cannot be accomplished. The informational requirements and restrictions of these approaches are considered. In dealing with the question of what surface parameters can be recovered locally from image shading, it is shown that, at most, shading determines relative surface curvature, i.e., the ratio of surface curvature measured in orthogonal image directions. The relationship between relative surface curvature and the second derivatives of image irradiance is independent of other scene parameters, but insufficient to determine surface shape. This result places in perspective the difficulty encountered in previous attempts to recover surface orientation from image shading.

Smith, G. B.↗

NASA NTRS1994

Generation of gear tooth surfaces by application of CNC machines

This study will demonstrate the importance of application of computer numerically controlled (CNC) machines in generation of gear tooth surfaces with new topology. This topology decreases gear vibration and will extend the gear capacity and service life. A preliminary investigation by a tooth contact analysis (TCA) program has shown that gear tooth surfaces in line contact (for instance, involute helical gears with parallel axes, worm gear drives with cylindrical worms, etc.) are very sensitive to angular errors of misalignment that cause edge contact and an unfavorable shape of transmission errors and vibration. The new topology of gear tooth surfaces is based on the localization of bearing contact, and the synthesis of a predesigned parabolic function of transmission errors that is able to absorb a piecewise linear function of transmission errors caused by gear misalignment. The report will describe the following topics: description of kinematics of CNC machines with six degrees of freedom that can be applied for generation of gear tooth surfaces with new topology. A new method for grinding of gear tooth surfaces by a cone surface or surface of revolution based on application of CNC machines is described. This method provides an optimal approximation of the ground surface to the given one. This method is especially beneficial when undeveloped ruled surfaces are to be ground. Execution of motions of the CNC machine is also described. The solution to this problem can be applied as well for the transfer of machine tool settings from a conventional generator to the CNC machine. The developed theory required the derivation of a modified equation of meshing based on application of the concept of space curves, space curves represented on surfaces, geodesic curvature, surface torsion, etc. Condensed information on these topics of differential geometry is provided as well.

Litvin, F. L.↗

NASA NTRSDate not supplied

Geometric Acoustics for Aircraft Noise Scattering

This paper discusses aircraft noise scattering by geometric acoustics, which consists of the basic features of sound propagation and reflection in rays or ray tubes, diffraction by smooth geometry in terms of surface creeping waves, and diffraction by abrupt geometry features such as the wing trailing edges. Based on the classic theories of these features, prediction methodologies can be constructed for aircraft noise scattering. The methodologies, however, require important modifications and extensions to account for unique features in aircraft noise applications, for both current conventional aircraft and future unconventional designs. These modifications and extensions include the derivation of a general reflection coefficient that contains the effects of surface geometry curvature, surface impedance, and mean flow. Corrections to the basic formulation of diffraction, both smooth geometry and sharp edges, are formulated to account for the finite dimensions of practical applications. For smooth geometry diffraction, a second order correction is used to continuously transition from insolified to shadow zones and an approach is presented to compute the properties of the geodesic path of surface wave propagation. A model is developed to make use of the ray propagation formulation for incoherent and partially coherent propagation and scattering, which is an important phenomenon in aircraft noise. Mean flow effect is also included in the methodology for low Mach number flows. Examples of calculations based on these theoretical developments are presented to illustrate the unique features in aircraft noise applications.

Yueping Guo↗

NASA NTRS1991

Asymptotic behavior of curvature of surface elements in isotropic turbulence

The asymptotic behavior of the curvature of material elements in turbulence is investigated using Lagrangian velocity-gradient time series obtained from direct numerical simulations of isotropic turbulence. Several material-element ensembles of different initial curvatures and shapes are studied. It is found that, at long times, the (first five) moments of the logarithm of characteristic curvature and shape factor asymptote to values that are independent of the initial curvature or shape. This evidence strongly suggests that the asymptotic pdf's of the curvature and shape of material elements are stationary and independent of initial conditions. Irrespective of initial curvature or shape, the asymptotic shape of a material surface is cylindrical with a high probability.

Girimaji, S. S.↗

NASA NTRS1989

Curvature effects on the stability of three-dimensional laminar boundary layers

The linear stability equations for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The system of equations is solved using a finite difference scheme in order to study the effects of streamline and surface curvature and compressibility on the stability of the flow past a swept wing. It is known that convex surface curvature can have a stabilizing effect on the laminar boundary layer. Conversely, concave surface curvature can be destabilizing. The magnitude of these effects for swept wings is determined. Results indicate that amplification rates and hence, N-factors, for the flow over the convex upper surface of a swept wing can be reduced by about 15 to 45 percent when curvature effects are included in the linear stability analysis. The results of the calculations show that concave curvature destabilizes crossflow type disturbances with a significant increase in amplification rate. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface.

Collier, F. S., Jr.↗

NASA NTRS1990

Convex curvature concept of viscous drag reduction

Experiments have indicated that for certain convex aerodynamic surface curvature ratios, wall-shear stresses remain low over considerable streamwide distances even after curvature is removed. The research whose progress is presently evaluated was first suggested by Bushnell (1983), who proposed that the convex-surface curvature be used in axisymmetric bodies to ascertain whether the viscous component of total drag is reduced. Attention is given to the evolution of the concept's implementation in an axisymmetric nose-body combination for passive viscous drag reduction.

Bandyopadhyay, Promode R.↗

NASA NTRS1986

Mean flow in turbulent boundary layers disturbed to alter skin friction

A comparative evaluation is made of recent developments in methods for the reduction of boundary layer drag, encompassing longitudinal surface riblets, 'outer layer' devices, (OLDs) and longitudinal convex surface curvature. The boundary layer of a surface with a longitudinal concave curvature is also studied, to complement the convex case results. The net drag reductions achievable by both riblets and OLDs are noted to be a rather modest 10 percent. Boundary layers exhibit asymmetric response to streamwise surface curvatures, with the response being slower for the case of a concave than a convex curvature.

Bandyopadhyay, P. R.↗

NASA NTRS1985

Impurity Extraction by Droplets

The goals are to model and to measure the phase equilibrium properties of a finely divided fluid containing a large number of chemically similar species. The objective is to develop an accurate, usable model for such phenomena as pollutant extraction of rain clouds, industrial separation in spray towers, and separation in emulsions. The project was designed as a hierarchy of complementary theoretical and experimental steps. A theory was developed to describe the segregation of complex impurities at the interface of a solvent. This phenomenon is important in phase behavior when a large fraction of molecules in a material are near an interface, the situation in a finely divided material. The theory will be modified to account for the effect of surface curvature on the surface tension. The study of mixtures differs from pure fluids not only because of the surface effects but also because composition differences between the droplet and the surrounding vapor can stabilize a droplet with respect to a bulk phase.

Morrison, G.↗

NASA NTRS1987

Investigation of generic hub fairing and pylon shapes to reduce hub drag

Reported are investigations of fairing configurations pointed toward substantially reducing hub drag. Experimental investigations have shown the importance of hub-fairing camber, lower-surface curvature, and relative size of the drag. The significance of pylon and hub fairings in combination have also been shown. Model test data presented here documented these findings, and also showed the effect of gaps and hub-fairing inclination angle on drag. From a drag standpoint, the best hub fairing had a circular arc, upper-surface curvature, a flat bottom surface, and 8.75% camber.

Stroub, Robert H.↗

NASA NTRS1987

Investigation of generic hub fairing and pylon shapes to reduce hub drag

This paper reports investigations of fairing configurations pointed toward substantially reducing hub drag. Experimental investigations have shown the importance of hub-fairing camber,lower-surface curvature, and relative size on the drag. The significance of pylon and hub fairings in combination have also been shown. Model test data presented here documented these findings, and also showed the effect of gaps and hub-fairing inclination angle on drag. From a drag standpoint, the best hub fairing had a circular arc, upper-surface curvature, a flat bottom surface, and 8.75 percent camber.

Stroub, Robert H.↗

NASA NTRS1989

Thin film deployable reflector model for ET gamma ray imaging telescope system (ET-GRITS)

The Marshall Space Flight Center is developing a thin film reflector for a Gamma Ray Imaging Telescope System (GRITS) using the Shuttle External Tank (ET). The concept is to install an inflatable reflector in the ET that could be transferred from the orbiter in orbit. This is a study of a scale model reflector for the ET GRITS application. The approach is to form 1/2 mil film into a spherical mirror mounted on a seven-foot diameter metal ring. The ring mount is sealed and slightly evacuated to pressurize the film into shape. Several different fabrication techniques were investigated using seamed gore designs to form the reflector. Also studied was casting a film into a seamless circular sheet. The goal for this model was to achieve a one milliradian (rms) surface curvature error over 90 percent of the reflector area. This curvature was measured by a laser scanning instrument. The results show how different reflector designs and fabrication techniques contribute to surface curvature and focusing errors.

Huegele, Vinson B.↗

NASA NTRS2011

Computational Analysis of the G-III Laminar Flow Glove

Under NASA's Environmentally Responsible Aviation Project, flight experiments are planned with the primary objective of demonstrating the Discrete Roughness Elements (DRE) technology for passive laminar flow control at chord Reynolds numbers relevant to transport aircraft. In this paper, we present a preliminary computational assessment of the Gulfstream-III (G-III) aircraft wing-glove designed to attain natural laminar flow for the leading-edge sweep angle of 34.6deg. Analysis for a flight Mach number of 0.75 shows that it should be possible to achieve natural laminar flow for twice the transition Reynolds number ever achieved at this sweep angle. However, the wing-glove needs to be redesigned to effectively demonstrate passive laminar flow control using DREs. As a by-product of the computational assessment, effect of surface curvature on stationary crossflow disturbances is found to be strongly stabilizing for the current design, and it is suggested that convex surface curvature could be used as a control parameter for natural laminar flow design, provided transition occurs via stationary crossflow disturbances.

Malik, Mujeeb R.↗

NASA NTRS1993

Linear stability of three-dimensional boundary layers - Effects of curvature and non-parallelism

In this paper we study the effect of in-plane (wavefront) curvature on the stability of three-dimensional boundary layers. It is found that this effect is stabilizing or destabilizing depending upon the sign of the crossflow velocity profile. We also investigate the effects of surface curvature and nonparallelism on crossflow instability. Computations performed for an infinite-swept cylinder show that while convex curvature stabilizes the three-dimensional boundary layer, nonparallelism is, in general, destabilizing and the net effect of the two depends upon meanflow and disturbance parameters. It is also found that concave surface curvature further destabilizes the crossflow instability.

Malik, M. R.↗

NASA NTRS1991

Tactile discrimination and representations of texture, shape, and softness

We present here some of the salient results on the tactual discriminabilities of human subjects obtained through psychophysical experiments, and the associated peripheral neural codes obtained through electrophysiological recordings from monkey single nerve fibers. Humans can detect the presence of a 2 micron high single dot on a smooth glass plate stroked on the skin, based on the responses of Meissner type rapidly adapting fibers (RAs). They can also detect a 0.06 micron high grating on the plate, owing to the response of Pacinian corpuscle fibers. Among all the possible representations of the shapes of objects, the surface curvature distribution seems to be the most relevant for tactile sensing. Slowly adapting fibers respond to both the change and rate of change of curvature of the skin surface at the most sensitive spot in their receptive fields, whereas RAs respond only to the rate of change of curvature. Human discriminability of compliance of objects depends on whether the object has a deformable or rigid surface. When the surface is deformable, the spatial pressure distribution within the contact region is dependent on object compliance, and hence information from cutaneous mechanoreceptors is sufficient for discrimination of subtle differences in compliance. When the surface is rigid, kinesthetic information is necessary for discrimination, and the discriminability is much poorer than that for objects with deformable surfaces.

Srinivasan, M. A.↗

NASA NTRS1989

A new airfoil design concept

The present airfoil design concept is based on utilizing unconventional geometry characteristics near the airfoil trailing edge which include a finite trailing edge thickness, strongly divergent trailing edge upper and lower surfaces, and high surface curvature on the lower surface at or near the lower surface trailing edge. This paper presents computational analyses of airfoils and a wing utilizing the concept, airfoil validation wind tunnel test results of several configurations, and wing-validation wind tunnel test results for a complete wing design. In addition to validating the concept, the airfoil and wing testing provided additional detailed data to better understand the aerodynamic advantage of such an unconventional trailing edge configuration. It is demonstrated that the concept represents a significant step in airfoil technology beyond that achieved with the Supercritical Airfoil. This concept provides the aerodynamicist an additional degree of design freedom and flexibility previously unrecognized.

Henne, P. A.↗

NASA NTRS2000

An Efficient Inverse Aerodynamic Design Method For Subsonic Flows

Computational Fluid Dynamics based design methods are maturing to the point that they are beginning to be used in the aircraft design process. Many design methods however have demonstrated deficiencies in the leading edge region of airfoil sections. The objective of the present research is to develop an efficient inverse design method which is valid in the leading edge region. The new design method is a streamline curvature method, and a new technique is presented for modeling the variation of the streamline curvature normal to the surface. The new design method allows the surface coordinates to move normal to the surface, and has been incorporated into the Constrained Direct Iterative Surface Curvature (CDISC) design method. The accuracy and efficiency of the design method is demonstrated using both two-dimensional and three-dimensional design cases.

Milholen, William E., II↗

NASA NTRS2007

Experiments in Transitional Boundary Layers With Emphasis on High Free-Stream Disturbance Level, Surface Concave Curvature and Strong Favorable Streamwise Pressure Gradient Effects

Experiments on boundary layer transition with flat, concave and convex walls and various levels of free-stream disturbance and with zero and strong streamwise acceleration have been conducted. Measurements of both fluid mechanics and heat transfer processes were taken. Examples are profiles of mean velocity and temperature; Reynolds normal and shear stresses; turbulent streamwise and cross-stream heat fluxed; turbulent Prandtl number; and streamwise variations of wall skin friction and heat transfer coefficient values. Free-stream turbulence levels were varied over the range from about 0.3 percent to about 8 percent. The effects of curvature on the onset of transition under low disturbance conditions are clear; concave curvature leads to an earlier and more rapid transition and the opposite is true for convex curvature This was previously known but little documentation of the transport processes in the flow was available

Simon, T. W.↗

NASA NTRS1985

Numerical Estimation of the Curvature of Biological Surfaces

Many biological systems may profitably be studied as surface phenomena. A model consisting of isotropic growth of a curved surface from a flat sheet is assumed. With such a model, the Gaussian curvature of the final surface determines whether growth rate of the surface is subharmonic or superharmonic. These properties correspond to notions of convexity and concavity, and thus to local excess growth and local deficiency of growth. In biological models where the major factors controlling surface growth are intrinsic to the surface, researchers thus gained from geometrical study information on the differential growth undergone by the surface. These ideas were applied to an analysis of the folding of the cerebral cortex, a geometrically rather complex surface growth. A numerical surface curvature technique based on an approximation to the Dupin indicatrix of the surface was developed. A metric for comparing curvature estimates is introduced, and considerable numerical testing indicated the reliability of this technique.

Todd, P. H.↗